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An Improved Adaptive Power Line Interference Canceller for Electrocardiography Suzanna M. M. Martens*, Massimo Mischi, S. Guid Oei, and Jan W. M. Bergmans, Senior Member, IEEE
Abstract—Power line interference may severely corrupt a biomedical recording. Notch filters and adaptive cancellers have been suggested to suppress this interference. We propose an improved adaptive canceller for the reduction of the fundamental power line interference component and harmonics in electrocardiogram (ECG) recordings. The method tracks the amplitude, phase, and frequency of all the interference components for power line frequency deviations up to about 4 Hz. A comparison is made between the performance of our method, former adaptive cancellers, and a narrow and a wide notch filter in suppressing the fundamental power line interference component. For this purpose a real ECG signal is corrupted by an artificial power line interference signal. The cleaned signal after applying all methods is compared with the original ECG signal. Our improved adaptive canceller shows a signal-to-power-line-interference ratio for the fundamental component up to 30 dB higher than that produced by the other methods. Moreover, our method is also effective for the suppression of the harmonics of the power line interference. Index Terms—Adaptive estimation, adaptive signal processing, electrocardiography, interference suppression, phase locked loops.
Fig. 1. The upper plots show the transfer (left) and impulse response (right) of a second-order IIR notch filter. The lower plots show an ECG signal free of power line interference (left) and the ECG signal after notch filtering (right).
I. INTRODUCTION OWER line interference may be significant in electrocardiography. Often, a proper recording environment is not sufficient to avoid this interference. For a high quality analysis of the electrocardiogram (ECG), the amplitude of the power line interference should be less than 0.5% of the peak-to-peak QRS amplitude [1]. This corresponds to a signal-to-interference ratio (SIR) of about 30 dB. The SIR is defined as the power ratio between the ECG signal and the power line interference. SIRs between 0 and 40 dB are normally encountered with contact electrodes. With capacitive electrodes [2] the high source impedance can result in large amounts of power line interference and the SIR may be much smaller than 0 dB. The power line interference can contain higher harmonics in addition to the fundamental component. In this paper we denote by power line interference the combination of the fundamental power line interference component and the harmonics. For convenience of processing and analysis, the ECG signal is usually digitized. If the sampling frequency is sufficiently high,
P
Manuscript received July 12, 2005; revised April 3, 2006. Asterisk indicates corresponding author. *S. M. M. Martens is with the Department of Electrical Engineering, University of Technology Eindhoven, 5600-MB Eindhoven, the Netherlands (e-mail:
[email protected]). M. Mischi and J. W. M. Bergmans are with the Department of Electrical Engineering, University of Technology, 5600-MB Eindhoven, Eindhoven, the Netherlands (e-mail:
[email protected];
[email protected]). S. G. Oei is with the Department of Obstetrics and Gynecology, Máxima Medical Center, 5500-MB Veldhoven, the Netherlands (e-mail:
[email protected]). Digital Object Identifier 10.1109/TBME.2006.883631
the resulting digital signal preserves all the information of the analog one. Therefore, in the rest of the paper, all the signals are represented as a function of the discrete time . The interference is commonly modelled as an additive is the signal. Therefore, the measured corrupted signal and the interference , sum of the signal of interest i.e., . An ideal power line interference suppression method should eliminate the power line interferwhile preserving the ECG signal . Two different ence approaches have been proposed in literature for this purpose: notch filters [3] and adaptive interference cancellers [4], [5]. Notch filters reduce the power line interference by suppressing predetermined frequencies. Usually, an infinite impulse response (IIR) filter is adopted. The typical impulse response of a notch filter shows some ringing (see Fig. 1). When a steep QRS complex is the input of the notch filter, the impulse response ringing can be recognized in the filtered signal as shown in Fig. 1. The amplitude of the ringing in filters with a narrow suppression band is smaller than in wide suppression band filters, although the decay of the ringing is slower. Furthermore, the magnitude and phase spectrum of the ECG signal are less affected by narrow suppression band filters. Therefore, the suppression band of the notch filter should be as narrow as possible. However, this leads to problems whenever the power line frequency is not stable or not accurately known a priori; a mismatch between the suppression band and the power line frequency might lead to inadequate reduction of the power line interference.
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MARTENS et al.: IMPROVED ADAPTIVE POWER LINE INTERFERENCE CANCELLER FOR ELECTROCARDIOGRAPHY
Fig. 2. General structure of a signal model and an adaptive interference canceller.
Adaptive interference cancellers have a general structure as , , and are the interfershown in Fig. 2, where ence signal, the signal of interest, and the corrupted signal, recan be represented as a known spectively. The interference of the interference parameter vector , i.e., function . If is a sinusoid, for instance, the interference parameter vector may contain its amplitude and phase. An interis internally generated as a function ference estimate of the estimated parameter vector , i.e., . The error signal is the difference between the corrupted signal and the estimated interference , and it is processed by an adaptation subscheme in order to find an estimate of . The subscheme behavior depends on , the adaptation constant vector. It is common practice to assume and to be uncorrelated and configure the adaptation subscheme such is minimized [4]. that the mean-squared error (MSE) This is referred to as least mean square (LMS) estimation. After is an estimate for the signal of inconvergence, the error terest , which, in our case, is the ECG signal. In general, a maximum-likelihood estimator is desirable. This , where is the estimator that maximizes the probability is the dataset and is the parameter vector. This estimator has profitable bias and variance properties [6]. A least-squares is adapproach produces maximum-likelihood estimates if is not white, an approxditive, Gaussian, and white [7]. If imate maximum-likelihood behavior can be obtained by for instance applying an error filter. Error filtering is frequently used in audio and speech signal processing to suppress the frequency components of the corrupted signal that are outside the band of interest and to whiten the frequency components within the band of interest [8]. It has been shown by Widrow [4] and Glover [9] that once the parameter estimates have converged and are fixed, an adaptive power line interference canceller is approximately equivalent to a notch filter. A key feature of adaptive cancellers is the possibility of a fine-tuning to the exact power line frequency. When the power line interference does not show harmonics, this tuning can be achieved by using an external power line interfer-
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ence reference signal and estimating the amplitude and phase of the fundamental component [4], [10]. In contrast, Ziarani [5] proposed a more practical method that does not require an extension of the recording equipment. In this method, not only the amplitude and phase, but also the frequency is estimated. In addition, he also proposed an approach to reduce the harmonics of the power line interference. Although Ziarani’s method is very promising, there is a considerable margin for improvements. In this paper, we propose six important improvements. 1) The proposed adaptive canceller is designed in the framework of phase-locked loop (PLL) systems. These systems have been extensively investigated in literature [11]–[15] and applied to several types of radio communication receivers. Key properties and potential problems of such systems are widely reported. Many of these problems concern the acquisition of the PLL system. Acquisition is the initial phase of estimation in which synchronism is acquired with the signal that is estimated. When the acquisition has succeeded and the misadjustments between the parameter estimates and the actual parameters are small enough, the system enters the tracking phase. Based on this background, these problems are carefully considered and proper solutions are proposed and implemented. 2) The adaptation subscheme is modified such that the convergence rates for the parameters are approximately independent of the a priori unknown power line interference amplitude. This is very desirable for the prediction of the dynamic behavior of the estimates, especially when the power line interference amplitude is non-stationary. Without this improvement, the settings of the canceller need to be fine-tuned to the instantaneous characteristics , which is unpractical. of the corrupted signal 3) According to the PLL system theory, an appropriate value for is derived. It is based on the desired acquisition and tracking properties of the system. 4) The error filter is optimized. A high-pass filter with a fixed cut-off frequency of 80 Hz is a highly effective error filter for this application. This error filter is applied to the error signal and within the adaptation subscheme. 5) The adaptation process is blocked during large-amplitude . Large-amplitude segments of the signal of interest segments (e.g., QRS complexes) affect the power line parameter estimates and generate undesired transients. Scheer [16] and Ider [10] proposed an implementation of this blocking operation that was based on the detection of the QRS complexes. We propose a more general solution to control the adaptation blocking, which does not require QRS detection. 6) A novel solution is proposed and tested for the reduction of the harmonics. Rather than using a different error signal for each harmonic, a joint error signal, which is based on the result of all the harmonic adaptation loops, is used. In this way, the adaptation process for one harmonic is not influenced by the energy of the other harmonics. As a result, the adaptation is only regulated by the difference and , so that the accuracy of the latter is between significantly improved.
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The net result of these improvements is a simple, generic, and highly powerful technique for the suppression of the power line interference in ECG recordings. We compare our improved adaptive power line interference canceller (IAC) to the canceller proposed by Ziarani [5] and a narrow and wide notch filter for the reduction of the fundamental power line interference component in ECG recordings. The results show that the value of the adaptation constant vector proposed by Ziarani for the canceller in [5] does not always lead to a successful acquisition phase. In fact, the canceller design is such that the optimal adaptation constant vector is dependent . In contrary, in our canceller scheme, the optimal value on of this vector is signal independent and properly chosen to optimize the dynamic behavior of the adaptation process. As a result, our IAC always shows an effective acquisition phase, inde. In the tracking phase, pendently of the characteristics of the proposed IAC performs significantly better than the notch filters. The IAC produces a cleaned ECG SIR that is up to 30 dB larger than that produced by notch filters. Moreover, our method shows excellent convergence properties also for harmonics. II. METHODS A. Least Mean Square Estimation In Fig. 2, every
yields an error
(1) where represents the residual interference in the error signal. If coincides with , and contains purely the signal of interest . In the presence of a parameter misadjustment , . Small paare visible in the error signal (see, rameter misadjustments also, Appendix II) as
(2) Here,
is referred to as a signature vector and is defined as
(3) , the error signal is related to by means Apart from of the signature vector and, therefore, it is indicative of the parameter misadjustment. As a consequence, the MSE decreases when the parameter misadjustment and are uncorrelated, becomes smaller, provided that i.e., . Therefore, the minimalization of can be used as a criterion for setting . This corresponds to a least-squares estimation [4]. For small parameter misadjustments the minimum of can be determined by locating the zero crossing of the gradient vector , given by
(4)
The gradient vector in (4) serves as an estimate for the parameter misadjustment vector . A least-squares estimation of corresponds to a search for the value of for which the crossand is zero. In real-time applicorrelation between cations, the implementation of (4) is not possible and adaptive closed-loop schemes are adopted. In these schemes, instantafor can be used [17], i.e., neous estimates (5) is proportional to , In (5), the misadjustment estimate introduces an additive disturbance to while the term the estimation of . This disturbance results in fluctuations of the parameter estimate vector around its steady-state value, referred to as gradient noise. The parameter vector is updated as given in (6) [17], i.e., on the basis of
(6) is a diagonal matrix with the elements of the adapwhere on the diagonal. Large values for the tation constant vector components of lead to faster convergence at the cost of a reduced accuracy of the estimates, i.e., of increased gradient noise. In this LMS estimation procedure, two phases can be distinguished: an acquisition and a tracking phase. In the acquisition phase, the parameter misadjustments can still be large so that (2) is not applicable and misadjustment estimators as given in (5) do not necessarily provide optimum control information. In the tracking phase, the misadjustments are small and their estimators work reliably [18].
B. System Model Initially, we only consider the fundamental component of the power line interference (the cancellation of harmonics is addressed in Section II-F). Fig. 3 shows the signal model and the proposed adaptive interference canceller. The variables , , and are the power line interference signal, the ECG signal, and the corrupted ECG signal. is modelled by an oscillator The power line interference (OSC) and a multiplier as given in (7), with , , and representing the power line amplitude, nominal frequency in radians per sampling interval, and phase in radians, respectively
(7) The actual power line frequency may deviate from the nominal corpower line frequency . A small frequency deviation becomes a responds to a time-varying phase. In this case, function of , i.e.,
(8)
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Fig. 3. Corrupted ECG signal model and proposed adaptive canceller of the fundamental component of the power line interference.
where is a fixed phase. The parameter vector estimate contains an estimate for the amplitude and phase i.e.,
Fig. 4. Corrupted ECG signal model and proposed modified adaptive canceller of the fundamental component of the power line interference.
,
(9) The interference estimate
is expressed as
As a result, the dynamic properties of the canceller in Fig. 3 are dependent on the estimated power line interference amplitude, resulting in a highly unpredictable adaptation process. This can be easily recognized if the expected value of the parameter misin (5) is considered for small amadjustment estimate or , i.e., plitude or phase parameter misadjustments
(10) (14) Using (1), the error signal can be expressed as
(11) An LMS estimation procedure as given in (6) can be used to , where obtain
(12) and are derived in Section II-C. Appropriate values for The adaptation of is only allowed when the updated is positive, i.e., when it leads to a positive amplitude estimate. In this way, we force the amplitude estimate to converge to a positive value and eliminate ambiguities in the parameterization. defined in (3) becomes The signature vector
As unpredictable adaptations may occur, the scheme in Fig. 3 is revised and the control on the adaptation process increased. The phase loop scheme is modified in order to improve the conand to reduce the dependency trol of the frequency deviation of the loop dynamics on variations of the amplitude . The resulting modified canceller is shown in Fig. 4. In order to improve the control of the frequency deviation , the first-order phase loop is replaced by a second-order PLL, i.e., the loop is divided into two processes for the separate estimation of and , respectively. For the latter, is introduced. The result is a loop an adaptation constant is filter LF whose transfer function in the domain given by
(15) (13) An appropriate value for
is derived in Section II-C.
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In order to reduce the dependency of on , a modified version of the signature vector given in (13) is introduced, i.e.,
(16)
where
is substituted by a normalizing term equal to . For (tracking phase) the use of the normalizing term leads to an expected value of the misadjustment that is approximately independent of estimate vector the power line interference amplitude
(17) and do not afAs a result, the amplitudes of both fect the dynamic behavior of the system. When the condition is not fulfilled, the approximation in (2) is not correct. Therefore, (14) does not apply and the use of the factor in (16) does not remove the dependency of the phase misadjust. This may cause problems in situations ment estimate on is very small or rapidly changing. In particular, if a where leads to inaccurate parameter estimates, acquisition small problems can be expected for the PLL when rises again. can be This problem during small amplitude periods of solved by limiting the frequency deviation estimate to a predefined interval. We assume that the maximum power line interference frequency deviation of the fundamental component is 4 Hz. Based on this assumption, the frequency deviation estimate is updated only for . Although may result in unreliable phase and frethe condition quency deviation estimates, they have no significant impact on the canceller performance if the canceller maintains . In this paper, we will specifically consider two extreme cases, to i.e., a step-fall of the power line interference amplitude zero, and an amplitude step-rise from zero to a value larger than zero. C. System Characteristics The amplitude loop in Fig. 4 is a first-order system and can be characterized by its adaptation time constant expressed in sampling intervals. With a first-order approximation, is related as to (18) The PLL in Fig. 4, on the contrary, is a second-order system (see Appendix I). Despite being in the discrete domain, for a sufficiently high sampling frequency, we can characterize the loop by a damping ratio [dimensionless] and a natural frequency [rad/sampling interval], which are related to and as (19) (20)
(18), (19), and (20) are derived in Appendix I. In general, an accurate parameter estimation requires small and should be chosen as small values of . Therefore, as possible. However, the tracking of time-varying parameters demands large values of . Our measurements show that the power line interference amplitude alternates between long periods in which it is approximately constant and sudden variations due, for instance, to motion artifacts. Therefore, should be large enough to guarantee a sufficient accuracy for the amplitude estimate, and small enough to adequately respond to step variations in the power line interference amplitude. The time constant is set equal to 0.13 s of 400 Hz, corresponds to which, for a sampling frequency 50 sampling intervals. are optimized with respect to the The settings for and stability of the power line interference frequency. In PLL systems, acquisition is an important issue. The PLL is referred to as is equal to the frequency of in-lock, when the frequency of . When the PLL is initially out of lock, the acquisition phase can be difficult. However, it has been shown that PLL systems (without an amplitude adaptation loop) lock up almost instantaneously if the maximum frequency difference between and is sufficiently small [11]. This fast acquisition applies to frequency differences up to a certain threshold, which is re[11]. In practice, ferred to as lock-in frequency damping factors in the order of 1 are commonly used. In our , , and a sampling fredesign we use quency . As a result, we obtain radians per sampling interval. This corresponds to the assumed maximum frequency deviation of 4 Hz, independent of the sampling frequency. In the presence of an amplitude loop, the PLL and amplitude loop can be expected to interfere with each other for large parameter misadjustments (acquisition phase). As a result, the acquisition behavior can deviate from the pure PLL theory described above. In Section III-A, the acquisition behavior of the canceller is studied in worstcase situations. D. Error Filtering Although is the signal of interest in our system, it affects the accuracy of the estimate of . This signal appears in the error signal and distorts the misadjustment estimate (gradient noise) as shown in (2) and (5). This undesirable effect is less pronounced for small convergence rates [18], i.e., for large and small . However, and have been set according to the desired acquisition and tracking properties for the parameter estimates, as discussed in Section II-B. In addition to the gradient noise generation, due to the non-white frequency spec, the LMS solution does not correspond to a maxtrum of imum-likelihood estimation. on the canThe negative effects of the non-white signal celler performance are reduced by means of a so-called error in order to apfilter, which is used to filter the error signal proximate a maximum-likelihood estimation. This filter is dethat are signed to suppress the frequency components of and to whiten the frequency outside the frequency band of within this frequency band. Our simulations components of show that a second-order IIR high-pass filter, having a cut-off
MARTENS et al.: IMPROVED ADAPTIVE POWER LINE INTERFERENCE CANCELLER FOR ELECTROCARDIOGRAPHY
Fig. 5. The left plot shows the magnitude of a second-order IIR high-pass error filter with cut-off frequency at 80 Hz and unit gain at 50 Hz. The right plot shows the ECG signal s(k ) of Fig. 1 and the resulting signal s (k ) after passing s(k ) through this error filter.
frequency between 40 and 150 Hz is a suitable error filter for ECG signals. This filter is scaled to produce a unit gain at the nominal power line interference frequency, so that the dynamic properties of the system are not affected. Fig. 5 shows an ECG signal before and after filtering with the proposed error filter . in (5) to zero. The IAC acts to drive the average value of If is filtered by a linear filter, such as the introduced error filter, also the signature vector (its derivative with respect to ) is filtered by the same filter. Therefore, for a correct use of , i.e., the filtered version of the (modified) signature (5), vector, should be used. As a result, the misadjustment estimate in (6) is replaced by the modified misadjustment esvector timate vector
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Fig. 6. The left plot shows the magnitude of a comb filter (f = 400 Hz, w = 50 2=f , = 8). The right plot shows a corrupted ECG signal d(k) with SIR = 0 dB and the resulting signal d (k ) after passing d(k ) through the comb filter. The dashed lines indicate the threshold values and .
1
0
preserving a large amount of the ECG signal in the corrupted (see Fig. 6). The transfer function is given by signal (22) where
is the rounded value of . Notice that for and for frequency deviations the notches of the comb filter are shifted with respect to the power line interference frequencies. This results in the presence of a residual power line . interference in , , and the standard deviations We denote by , , and , respectively. Furthermore, we of the amplitude of the residual power line interdenote by ference in . As and are uncorrelated, . Two cases may occur. If and , and , leading to then
(21) where
is the error signal after filtering with
.
E. Adaptation Blocking Although, as shown in Fig. 5, an error filter can suppress a large part of the ECG signal, the amplitude of QRS complexes after filtering may still be much larger than the power line interference amplitude when the SIR is large. QRS complexes occur at the frequency of the heart rate, i.e., approximately every second, and last at most 0.10 s [19]. In addition to QRS complexes, an ECG signal can display segments with large amplitude noise. For instance, abrupt shifts in the baseline can occur due to electrode contact noise [20]. These large-amplitude segments unsettle the parameter estimates, resulting in temporary gradient noise. By blocking the adaptation process during large-amplitude segments, the gradient noise can be significantly reduced. The application of this procedure involves the detection of shows a large amplitude. For this purthe segments where pose, we can monitor the error signal, which is a good estimate when the canceller is in the tracking phase. This refor quires that also the stage of adaptation is monitored to detect the , the tracking phase intervals. In contrast to the error signal is not affected by the stage of adaptation. corrupted signal Unfortunately, this signal contains the power line interference can be used to supsignal. However, a simple comb filter press the power line interference frequency components while
(23) If and/or , then the comb filter does not completely remove the power line interference. In this case, and . Therefore
(24) to a threshold value . We compare the amplitude of When exceeds , the adaptation process is blocked for the iterations that fall within a period of 0.05 s before and after the occurrence. This will insert a small delay in the system which is nevertheless negligible compared to the ECG complex duration. To ensure that is such that the blocking is not trig, should gered by the residual power line interference in . A suitable value for is, therefore be larger than (25) Assuming an ergodic process, we calculate samples, i.e., window of
over a sliding
(26)
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For , should be as small as to permit variations to be followed with sufficient speed. However, should not depend on the part of the ECG complex that is covered by the window. Therefore, each window should contain at least one QRS complex. Assuming the adult heart rate to be at least sampling intervals is an appro60 beats per minute, priate window length. F. Processing of Harmonics In this section we extend the system in order to suppress also the harmonics of the power line interference. If denotes the (including the fundamental comnumber of harmonics in ponent), the power line signal can be represented as the sum of sinusoids, each one with different amplitude , nominal and phase frequency
Fig. 7. Performance of the IAC on a real ECG recording containing power line interference components at 50 and 150 Hz. The upper plots show the corrupted recording and the lower plots the cleaned recording.
(27) applies to the fundamental power line interferThe case of the power line interference component. An estimate ence consists of the sum of the estimates for all the sinusoids. Therefore, amplitude and phase must be estimated for each harcan be realized by subtracting monic . A joint error signal . After error filthe sum of all the harmonic estimates from results in the filtered error signal , which is tering, used for the adaptation. This approach differs from [5] where an error signal is defined for each harmonic as the difference beand the estimate for that specific harmonic. The use tween of different error signals increases the contribution of undesired signal components in the parameter misadjustment estimates, which become dependent on the energy of the other harmonics. Therefore, we propose to use a joint error signal for the estimation process of each harmonic. The modified signatures to be used are given by
(28)
scheme to compensate for the different magnitudes of the error at the harmonic frequencies, i.e., filter transfer function . G. Implementation and Initialization In summary, the implementation of the adaptation algorithm, including the processing of the harmonics of the power line interference, consists of the equations (30) (31) (32) which are used for the generation of the power line interference as given in (27). In (30)–(32), the values of , estimate , and are derived from the system characteristics given in Section II-C, whereas the modified misadjustment estimates and are defined by (29) and (28). The initial , , , conditions are given by , and . This initial value for is due to the lack of a power line interference amplitude estimate at the initialization of the IAC.
where
for and for . Therefore, the modified misadjustment estimate vector is given by
(29) In the ideal case, the adaptation loops of all parameters are not coupled, i.e., a misadjustment in one loop does not affect the steady-state solution of another loop. This applies to systems in which all signatures are orthogonal and this desirable property holds for our system as shown in Appendix II. The choice for , , and is the same for all parameters. The error filter proposed in Section II-D is applied to the error signal and all signatures. This implies the use of scaling factors in the adaptation
III. RESULTS Fig. 7 shows a real ECG recording corrupted with power line interference, including one harmonic component (150 Hz), and the corresponding cleaned recording resulting from the IAC. A complete cancellation of the interference can be noticed after 0.5 s. For an accurate quantification of the cancellation performance, the SIR at the input and output of the canceller must be known. In Section I the SIR is defined as the ratio between the and the power line interference power of the ECG signal . From now on we refer to this quantity as the input SIR . As a performance measure of the adaptive interference , defined cancellation scheme we adopt the output SIR
MARTENS et al.: IMPROVED ADAPTIVE POWER LINE INTERFERENCE CANCELLER FOR ELECTROCARDIOGRAPHY
as the ratio between ECG signal power in the error signal interference power
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and residual line , i.e.,
(33) where
. Notice that in general and cannot be measured objectively as we do not know , , and . Therefore, the cancellation performance is assessed by a specific simulation. A recorded ECG signal whose frequency spectrum indicates the absence of power line interference is selected. In this way, a clean ECG signal is obtained. . A set of 50-Hz Peak-to-peak QRS amplitude is about 1000 power line interference signals with amplitudes ranging from to 1500 and frequency deviations ranging 15 from 0% to 8% is synthesized. No harmonics are synthesized. Adding this set of synthetic power line interference signals to the clean ECG signal results in a set of corrupted ECG signals with of 20, 0, and 20 dB. In Section III-A we compare the acquisition performances of our improved adaptive canceller (IAC), a simpler adaptive canceller in which the error filtering and adaptation blocking are excluded (SAC 1), the same simple adaptive canceller with error filtering (SAC 2), and the adaptive canceller proposed in [5] (AC). Their acquisition behavior is analyzed for two identified worstcase situations that may occur. In the first situation, the system is initially in lock. At some point in time, the power line interference amplitude drops to zero. From this point on, the dynamic behavior of and becomes unpredictable as explained in II-B. However, if is small enough, the effect of this out-of-lock condition of the PLL on the system performance is negligible. In the second situation, a power line interference step-rise from zero occurs while the PLL is out of lock due to the first worstcase situation. Therefore, the frequency deviation misadjustment may be as large as 4 Hz. This the the most difficult acquisition situation for the PLL as discussed in Section II-C. In Section III-B, the tracking performance of the IAC, SAC 1, SAC 2, AC, a wide notch filter (WNF), and a narrow notch filter (NNF) are compared. The wide notch filter is designed such that a 10 dB attenuation is achieved at the lock-in threshold . The narrow notch filter has a 10 dB frequency, i.e., . The resulting transfer function in attenuation at the domain is given in (34) [21], where and for the wide and narrow notch filter, respectively, and is the inverse of the magnitude of the notch filter at
(34)
A. Acquisition Performance The two worstcase situations are simulated. In the first simulation (simulation 1), the amplitude of the power line interferdrops from 150 to 0 ence in
Fig. 8. Cleaned signal e(k ) in the two worstcase acquisition situations for the SAC1 (top), the SAC2 (middle), and the IAC (bottom).
, while . In the second simulation (simulation 2), the amplitude of the power line interferrises from 0 to 150 ence in , while the initial misadjustment of the frequency deviation is maximal ( and ). The initial phase misadjustment is random. For both simulations the starting point with respect to the ECG signal is fixed on the QRS complex which results in the largest gradient noise (worst case). Each simulation is repeated 1000 times. Our simulations show that for the AC the loop gains have to be fine-tuned to the corrupted signal. In fact, the proposed loop gains in [5] do not lead to convergence for our corrupted signals. Therefore, the AC is not considered for further comparisons. for the SAC1, SAC2, and Fig. 8 shows the cleaned signal IAC for all the simulations. In simulation 1, the parameters of the SAC1, SAC2, and IAC always converge within 0.5 s. However, the parameters of the SAC1 display a large amount of gradient noise due to QRS com. plexes resulting in a residual power line interference This effect is less pronounced for the SAC2 that comprises an error filter. The IAC amplitude always converges to within 0.5 s. Although the phase and frequency deviation estimates are not reliable (not shown here), for the phase and frequency deviation estimates are irrelevant. is After convergence, the residual power line interference to be larger than 30 dB. as small as to permit the In simulation 2, the acquisition is more difficult for all cancellers. The IAC and the SAC2 always converge within 1.5 s, while the PLL of the SAC1 goes out of lock frequently. However, only the IAC convergence always results in an larger than 30 dB.
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TABLE I PERFORMANCE FOR INCREASING FREQUENCY DEVIATIONS
TABLE II PERFORMANCE FOR INCREASING
SIR (
(SIR = 0 dB)
=w
= 0%)
Fig. 10. ECG signal corrupted with synthetic power line interference including equals the fundamental component and one harmonic (upper plot). The 20 dB and =w equals 8%. The cleaned signal resulting from IAC is shown . below
SIR
(SIR = 36 dB)
shows an ECG signal corrupted with a power line interference signal including the fundamental component and one harmonic and ), and the corresponding ( cleaned signals obtained via the IAC. IV. CONCLUSION
Fig. 9. The corrupted ECG signal (upper left) and the cleaned signals resulting (lower left), the WNF with from the IAC with (upper right), and the NNF with (lower right) are equals 0 dB and =w equals 0.8%. The WNF eliminates shown. The the power line interference, but affects the ECG spectrum significantly (e.g., the QRS amplitude is reduced), while the NNF is not able to eliminate the power line interference.
15 dB
SIR
SIR
= 37 dB
SIR
= 11 dB
SIR
=
B. Tracking Performance The tracking performance of the IAC, SAC1, SAC2, WNF, and NNF are compared for different power line frequency devi, respectively. Performance is exations and for different and is calculated during the tracking pressed in terms of phase (see Tables I and II). The results show that the IAC proof about 35 dB, while duces cleaned signals having an simpler adaptive cancellers and notch filters are limited by an upper bound of 25 dB. As expected, for increasing frequency deviations the IAC is significantly larger than that produced by the other methods. and Fig. 9 shows the corrupted signal ( ) and the corresponding cleaned signals obtained by means of the WNF, the NNF, and the IAC. Fig. 10
This paper proposes an improved adaptive canceller for the suppression of the power line interference in ECG recordings. The canceller tracks the amplitude, phase and frequency of the fundamental component and of the harmonics of the power line interference. It comprises a second-order PLL so that frequency deviations can be handled. The error filter that is implemented in the canceller reduces the gradient noise caused by the ECG signal and the baseline wander. The blocking of the parameter adaptation further reduces the gradient noise in the presence of large amplitude segments like the QRS complex. Our simulations show a stable acquisition behavior of the IAC even in the worst conditions. The acquisition phase usually takes less than 1.5 s. This implies that for a sudden variation in amplitude, phase, and frequency of the power line interference, the system may need about 1.5 s to adapt to the new situation. During these events, the power line interference suppression may be inadequate. The detection of these events may be performed by means of a lock-indicator whose implementation will be considered in the future. The acquisition performance might be further improved by means of phase-and-frequency detectors as in [22]. The implementation of such a detector in the case of harmonics requires the employment of additional filters. Given the small frequency deviations of the power line interference and the satisfactory results of the proposed system, this solution has not been included in the final implementation. The results of our simulations in the tracking phase indicate that our improved adaptive canceller IAC yields ECG signals with an SIR that is larger than the desired level of 30 dB, independent of the input SIR. This signal quality is adequate to allow a highly accurate ECG analysis [1]. The performance of the IAC is independent of the power line interference frequency
MARTENS et al.: IMPROVED ADAPTIVE POWER LINE INTERFERENCE CANCELLER FOR ELECTROCARDIOGRAPHY
Fig. 11. Parameter-domain models for amplitude (left) and phase (right).
deviation. The error filtering and the adaptation blocking procedures significantly improve the performance of the adaptive canceller. The notch filter performance deteriorates as the power line interference frequency deviation increases. This effect is more pronounced in the narrow notch filter. However, for a frequency , the narrow notch filter performs sigdeviation nificantly better than the wide notch filter because the ECG signal is less affected by the filtering distortions. The output SIR for notch filters does not depend on the input SIR when . The comparison between the notch filters and the proposed IAC in the tracking phase shows that the IAC performs better in all situations, especially for increasing frequency deviations. As shown in Fig. 10, the IAC can also suppress the harmonics of the power line interference with the same efficiency as for the fundamental component. In fact, using a joint error signal for each harmonic reduces the gradient noise introduced by the energy of the other harmonics. In conclusion, the proposed IAC is a highly adequate technique for the suppression of the power line interference in ECG recordings and is to be preferred to notch filters. The operations integrated in this technique, such as error filtering and adaptation blocking, make the IAC insensitive to baseline fluctuations and large-amplitude segments. Therefore, the IAC is also suitable for dynamic applications like for instance exercise ECG. In addition, with some slight modifications the IAC would be equally applicable to other types of corrupted biomedical recordings such as the electromyogram (EMG) and the electroencephalogram (EEG). APPENDIX I RELATION BETWEEN LOOP GAINS AND SYSTEM PARAMETERS Dynamic properties of the amplitude and phase loop can be obtained by using parameter-domain models [18]. Fig. 11(a) and 11(b) shows the parameter-domain models for the amplitude and phase loops, respectively. In these models, the approxas given in (14) is used, i.e., imation for
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of the dynamic-behavior parameters, we prefer the use of the Laplace domain over the -domain. The Laplace domain provides a system representation that can be directly compared with standard first- and second-order representations of real linear systems in the continuous domain. The transformation from the -domain into the Laplace domain is given by , where is the sampling period. Therefore, if is sufficiently small, a discrete system can be represented in the continuous Laplace domain by the first-order Taylor approximation . , , , We denote the Laplace transforms of and by , , , and , respectively. Therefore, the models of Fig. 11(a) and 11(b) can be approximated in the Laplace domain by the transfer functions and as given by
(35) (36) The amplitude transfer function of (35) is of the first-order. A unit step input to the system results in the outputs in the Laplace domain and in the time domain
(37) (38) Therefore, for sufficiently small, the time constant [in sampling intervals] of the amplitude loop is expressed as given in (18). The phase transfer function is of the second-order. A standard expression for second-order systems is given in (39), where and are the damping factor and the natural frequency of the system
(39) Equating (36) and (39) along the imaginary axis, we obtain the , , relationships (approximations for small) between , and [in radians per sampling interval] as given in (19) and (20).
APPENDIX II ORTHOGONALITY OF SIGNATURES For simplicity, we first consider a single-parameter estimation. For small, can be represented by a first-order Taylor approximation as given by
The systems are defined in the discrete time domain. However, for a characterization that is aimed at the interpretation
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IEEE TRANSACTIONS ON BIOMEDICAL ENGINEERING, VOL. 53, NO. 11, NOVEMBER 2006
where As a result,
is the signature. can be approximated as
We denote the amplitude and phase misadjustment estimates of and , respectively. As a result, harmonic with and are equal to the expected values of
Apart from the noise term , the error signal contains a component that is proportional to , and whose shape . is defined by For a multi-parameter estimation, each parameter misadjustcontributes to the error signal and adds a component ment as shown in (40), where is the number of parameters1
(40) With the substitution of (40) in (5), an approximation of the is obtained, i.e., parameter misadjustment estimate
(44) Under the ergodicity assumption, the expected values of the periodic functions in (44) are given by the normalized time integral in one period. Moreover, the products and cross-products and cosines are equal to their between sines sums according to the Werner formulas. As a consequence, if the phase variations are negligible within one period, and in (44) only the terms differ from zero (i.e., the signatures are orthogonal) and the misand can be expressed as adjustments
(41) (45) where . As a consequence, , i.e., the mis, but adjustment estimate of , is not only depending on is also affected by the other parameter misadjustments, resulting in an undesired coupling between the adaptation loops. This situation is avoided if the signatures are orthogonal [23], i.e., for . For orthogonal signatures, the in (41) is equal to expected value of
(42) As a result, a misadjustment in one loop does not affect the steady-state solution of the other loops and the adaptation loops behave independently from each other. In our system, the misadjustment of each harmonic power line interference component is estimated by means of two signature components as given in (28), i.e., a sine (amplitude loop) and a cosine (phase loop) with equal arguments. Signatures for different harmonic adaptations have different frequencies. For simplicity we assume in (28) equal to 1 and the noise . We denote with and the amplitude and phase signatures of harmonic , respectively. In this case the error signal can be approximated by
(43) 1Notice
that (40) corresponds to (2).
A direct consequence of (45) is that the adaptation loops are not coupled in our system.
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[13] W. C. Lindsey, Synchronization Systems in Communication and Control. Englewood Cliffs, NJ: Prentice-Hall, 1972. [14] W. C. Lindsey and R. C. Tausworthe, A Bibliography of the Theory and Application of the Phase-Lock Principle Jet Propulsion Laboratory, Tech. Rep. 32-1581, 1973. [15] A. Blanchard, Phase-Locked Loops: Application to Coherent Receiver Design. New York: Wiley, 1976. [16] H. J. Scheer, “Line frequency rejection for biomedical application,” IEEE Trans. Biomed. Eng., vol. BME-34, no. 1, pp. 68–69, Jan. 1987. [17] S. Haykin, Introduction to Adaptive Filters. New York: Macmillan, 1984. [18] J. W. M. Bergmans, Digital Baseband Transmission and Recording. Boston, MA: Kluwer Academic, 1996. [19] A. C. Guyton and J. E. Hall, Textbook of Medical Physiology, 10th ed. London, U.K.: Saunders, 2000. [20] G. M. Friesen, T. C. Jannett, M. A. Jadallah, S. L. Yates, S. R. Quint, and H. T. Nagle, “A comparison of the noise sensitivity of nine QRS detection algorithms,” IEEE Trans. Biomed. Eng., vol. 37, no. 1, pp. 85–98, Jan. 1990. [21] P. S. Hamilton, “A comparison of adaptive and non-adaptive filters for reduction of power line interference in the ECG,” IEEE Trans. Biomed. Eng., vol. 43, no. 1, pp. 105–109, Jan. 1996. [22] R. C. D. Dulk, An Approach to Systematic Phase-Loop Design Universiteitsdrukkerij TU Delft, 1989. [23] B. Farhang-Boroujeny, Adaptive Filters. New York: Wiley, 1998.
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Massimo Mischi was born in Rome, Italy, in 1973. In 1999, he received the M.S. degree in electrical engineering from La Sapienza University of Rome. In 2002, he successfully completed a two-year Post-Master program in technological design, information and communication technology, at the Eindhoven University of Technology, Eindhoven, The Netherlands. In 2004, he received the Ph.D. degree from the Eindhoven University of Technology on cardiovascular quantification by contrast echocardiography. Currently, he is a Researcher with the Signal Processing Systems Group of the Eindhoven University of Technology. His research covers several medical signal processing topics and applications.
S. Guid Oei received the Ph.D. degree from Leiden University, Leiden, The Netherlands, in 1996. He is a Gynaecologist at Máxima Medical Center, Veldhoven, The Netherlands, and Professor in Fundamental Perinatology at Eindhoven University of Technology, Eindhoven, The Netherlands. He subspecialized in perinatology at Flinders University in Adelaide, Australia. Since 2003, he is head of the Department of Obstetrics and Gynaecology, Máxima Medical Center. In the same year he was appointed Professor in the Department of Biomedical Engineering, Eindhoven University of Technology. Since 2004, he is Medical Director of the Medical Education and Research Institute, Máxima Medical Center.
Jan W. M. Bergmans (M’95–SM’91) received the Ingenieur and Ph.D. degrees from Eindhoven University of Technology, Eindhoven, The Netherlands, in 1981 and 1987, respectively. From 1982 to 1999, he was with Philips Research Laboratories, Eindhoven, The Netherlands, working on signal processing for digital transmission and recording systems. In 1988 and 1989, he was exchange Researcher at Hitachi Central Research Laboratories, Tokyo, Japan. He is now Professor of Signal Processing Systems, Eindhoven University of
Suzanna M. M. Martens was born in Breda, the Netherlands, in 1980. In 2003 she received the M.S. degree in biomedical engineering from the Eindhoven University of Technology, Eindhoven, The Netherlands. She is currently working towards the Ph.D. degree in the Signal Processing Systems Group, Eindhoven University of Technology.
Technology.
